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We have performed numerical calculations to investigate the stability of multi-electron bubbles in liquid helium-4. In our calculations, for each bubble shape considered we flnd the equilibrium distribution of the electron gas on the inside surface of the bubble. For a stationary bubble, we flnd that whenever the pressure in the liquid is positive the bubble is unstable against flssion into two bubbles. We flnd that a moving bubble can be stable within a certain region of the pressure-velocity plane. At the high pressure boundary of this region, the bubble undergoes flssion, and on the low pressure boundary the bubble explodes.

Theory of the stability of multielectron bubbles in liquid helium